July 30, 2004

Incompetent calculator jockeys

I've noticed an interesting phenomenon in my math classes over the last couple of years, which has become more pronounced as the subject matter becomes (to some people) more difficult: the Desperate Calculator Jockey. This is the guy who never studies, is too lazy to do his homework, but somehow manages to struggle his way from one class to the next. He can usually be seen furiously punching formulae into a top-of-the-line TI-89 or its near-equivalent, expecting some magical insight into the problem from the resulting graph. While this approach may actually work in some instances, such as with a simple "differentiate this function" problem, the approach is an utter - and deserved - failure when the student is confronted with the dreaded applications problem (the so-called "word problem.")

Oh, my... this is where thinking skills are really tested, and where numerical prosthesis is nearly worthless. I love these problems: exercises in aircraft fuel vs range optimization, predictions of least-time photon transit through a non-vacuum medium (Snell's Law, an application of the Brachistochrone curve), calculations of marginal cost & maximization of profit, how to make the largest rectangular horse corral with a fixed length of expensive fencing... the good stuff. The Calculator Jockeys rarely know where to start decomposing a problem to its tractable constituents, instead, as usual, attempting to invoke an answer from the aether by keypunch.

I can pretty much tell from looking around a room who's faking it and who's getting it: those who are actually learning the calculus are learning with their pencils, which are constantly moving on paper. The fakers, on the other hand, are constantly pushing buttons. The joke's on the latter group: with the exception of actual symbolic manipulation packages such as Wolfram's Mathematica, hand calculators - to date - depend entirely on methods such as linear approximation. This means that the calculator jockey can actually get the wrong answer for a derivative of a function at a point on a curve, since the curve may not actually be differentiable at that point, but the linear approximation around that point of a secant line connecting points on either side of the original point may exist. Suckers.

Posted by Russell Whitaker at July 30, 2004 04:39 PM | TrackBack
Comments

Which is why you'll be a competent, passionate professional and they'll wonder what the hell to do with their lives in 10 year's time.

Posted by: Monica on July 30, 2004 08:13 PM

I noticed some things about my math classes over the years, too: that they were largely useless, given the rote-memorization technique and the fallibility of the average non-eidetic human brain's long term memory storage of stringently-memorized data.

When you're on your death-bed, will you look back on this rant and wonder whether you should have bothered expending so much energy spying on and judging others for their abilities in a class which, in all likelihood, less than 1% of your graduating class will ever use, or be able to use, for most of the rest of their lives? Probably not, as this incident will be far too unimportant to retain in memory by then.

So what's the point?

Is it that you want to convince the fakers to change their ways? To what end? Why should you care whether they're learning the way you are, or even learning at all? Are you personally involved with these people? If so, why not confront them with this information rather than posting it where your classmates will likely never encounter it, in a godforsaken blog in the deepest reaches of cyberspace? If you have no personal connection, how is their second-handing it through their life relevant to how you live yours?

William of Ockham would suggest that the simplest explanation - that you're a gloating blowhard - is the most likely to be true. I'm not sure about that. I will take my own advice, though, and stop concerning myself with the foolish actions of others. Ciao.

Posted by: Bobby Timmy on July 31, 2004 07:17 AM

Russell, my mother said the same thing in her own way. She, being another one of those "competent in everything she does" people.

While, as Timmy notes above, she never used calculus, she also never used the slide-rules that were all anyone had back when she was in school. She did it as you suggest, with pencil and paper, and an understanding of where to begin breaking problems down.

"Word" problems do seem to effect people as "terrible, awful", while doing nothing other than tying together language of words with language of numbers. Could it be that this is done far too little? That more interconnections betwixt these seemingly disparate languages would be a good way to improve thought processes? Could be why it's not taught in forced government school.

I don't find Timmy a surprise at all, someone who makes a large effort to say how he's not going to waste his time doing exactly what he's doing. Chortle. Don't erase it, a bad example is important.

Curt-

Posted by: Curt Howland on July 31, 2004 10:33 AM

Reminds me of a rant about Brazillian physics students in Richard Feynman's book Surely you're joking, Mr. Feynman. They were excellent at answering questions whose answers they had memorized, but worthless for any practical problem. There's an excerpt at http://www.exmormon.org/boards/honestboard/messages/783.html

Posted by: Bill St. Clair on August 1, 2004 05:19 AM

The last thing I remember doing with calculus: I needed to adapt Least Squares polynomial approximation for complex values, and to do that I essentially had to derive the method almost from scratch. (It was for a "conlang"-related project.)

Before that, let's see, I worked out where the dominant artifact spirals change in the "sunflower" pattern (plane and spherical - see the webpage).

Before that, hm, possibly something to do with Iterated Prisoners Dilemma game strategies. Dunno. Certainly nothing very practical in a long time, but I've had great fun with it.

Posted by: Anton Sherwood on August 9, 2004 06:11 PM

I understand that some people are very passionate about mathematics and believe in the strongest worth ethic, while shunning calculators for anything unless required. I think this is admirable, and I respect these individuals.

However, when I consider actually using these skills in business, I tend to believe that high proficiency with a calculator could create a greater efficiency and solve problems more rapidly. I know that professors can take their time and work everything out by hand, but when your boss wants an answer 'right now', I dont think he will be biased towards its source!

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